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Numbers k such that the distance from k^2 to the smallest triangular number >= k^2 is itself triangular.
1

%I #11 Sep 15 2024 14:03:56

%S 1,3,5,6,7,9,11,15,18,20,28,30,35,42,45,54,60,63,66,77,78,88,90,102,

%T 105,114,117,126,130,138,150,162,165,174,175,186,198,204,210,221,222,

%U 234,245,246,247,258,264,266,270,282,294,306,315,318,330,342,351,354,366,368,378,385,390

%N Numbers k such that the distance from k^2 to the smallest triangular number >= k^2 is itself triangular.

%o (PARI) is(n)=my(t=floor((sqrt(8*n^2)-1)/2)+1);t=t*(t+1)/2-n^2; my(tt=floor((sqrt(8*t)-1)/2)+1);(tt*(tt+1)/2==t)

%Y Cf. A230038.

%K nonn

%O 1,2

%A _Ralf Stephan_, Oct 08 2013